In the early days of the space program, we in the good ol' U.S.A put our astronauts on skyrockets, otherwise known as military missiles, and shot them off into space. We were forced to do this because the Soviet Union was launching cosmonauts quite regularly, and our civilian space program was pretty much a disaster. Now, what do you suppose a military missle is designed to do? It is, of course, supposed to get to its target as quickly as possible. This means the missile accelerates at a very high rate in order to attain a large speed in as short a time as possible. Newton's second law, from Chapter Two, says the net force acting on an object equals the object's mass times its acceleration,
(2.29) Fnet = ma.
So you see there has to be a large net force acting on an object of mass m in order for it to achieve a large acceleration. Because of the large accelerations involved, and to better relate acceleration to human sensation, jet fighter operations and the space program use "g"s to measure the acceleration and, through the proportionality between acceleration and force expressed by Eq. (2.29), the force experienced by the pilots and astronauts. One "g" is the acceleration of gravity at the Earth's surface (which, in this book, I take as 9.8 m/s2 or 32 ft/s2).
The force you experience as 1 g is the support force (due to, for example, the floor you are standing on) that holds you up against the force of gravity, that is, your weight. Should you be so unfortunate as to lose this 1 g support force, for example falling off the roof while adjusting the satellite dish, you will experience, briefly, the effects of 0 g: no support force. If you were lifting off the surface of the Earth in a rocket and experiencing 2 g's, you would feel as if you weighed twice as much as you normally do, just standing around in the kitchen waiting for dinner. To give you the sensation of 2 g's, you would need a support force, provided by your flight seat, that is twice your weight. Since you get 1 g by just hanging out with the usual 9.8 m/s2 acceleration of gravity that is always there, you must accelerate upward at 9.8 m/s2 to experience 2 g's. An excess, or net, force equal to your weight must therefore act on you to give you this upward acceleration. The net force acting on you is
Fnet = 2mg (upwards, due to your flight seat) - mg (downwards, your weight) = mg (net, upwards),
so that,
a = mg / m = g.
The 2mg force of the seat on your body gives you the sensation of "2 g's".
The facility of the "g" terminology is that it refers to the force you experience in multiples of your weight. We all regularly experience our own weight, a force of 1 g. If you were subjected to a force of 2 g's, as noted above, you would feel as if your weight had doubled. The large g's generated by the acceleration of a military missile may not be a problem for a nuclear warhead but was definitely a problem for the early Mercury and Gemini astronauts. (The first two Mercury Astronauts, Alan Shepard and Gus Grissom, had to endure forces up to 11 g's due to the use of the Redstone ballistic missile as a booster. This meant their flight seats exerted a force on them 11 times their actual weight! An astronaut weighing 150 pounds would feel as if he weighed 1650 pounds!! By Newton's second law, the astronauts experienced a net force 10 times their weight, accelerating them at the enormous rate of 98 meters per second every second. This is close to increasing your speed by one tenth of a kilometer per second every second or over 200 miles per hour every second! (I'd like to see somebody's 'Vette do that!) The subsequent Mercury flights used the Atlas booster, so that the astronauts on the following flights experienced forces of "only" 7.5-8 g's.) How did the astronauts prepare for such tremendous "g forces"? The medical teams spun them around in centrifuges, that's how.
(6.1) "Pat, I'd Like to Buy an ... Eeeeeeeee!!": Centripetal Acceleration
The Wheel of Fortune is technically pretty lame when compared to some of centrifuges used nowadays to train jet fighter pilots. Anyone who has ridden a merry-go-round or one of those carnival rides that swing you around in circles knows that going in a circle results in the experience of forces that grow stronger as the circular motion gets faster. Training facilities for jet pilots use this effect to simulate the extreme forces of jet fighter flight, and prospective pilots are often required to take what is sometimes called "cockpit physics", where they learn, among other things, the origin of the g forces they experience in training centrifuges.
To understand why a centrifuge can produce large forces on the object being swung around, you have to go back to the definition of acceleration: Acceleration is the time rate of change of velocity. This definition is expressed by the following equation,
(6.1) a = dv/dt.
For you non-technical students, this equation, in English, sta